I like a different explanation, which applies analogical thinking. Imagine, that instead of 3 doors there are 1000, and then 998 without a car are closed. I guess, even one clueless about stats and probabilities will understand, that "the other door" is the way. Unless s/he sees through the doors.

I also think, that imagining equal chances after the wrong door has been shown mean, that you ignore information.

Thank you for making think about this problem again!